Correction device for function generators



P 1953 P. T. NICKSON 2,652,195

CORRECTION DEVICE FOR FUNCTION GENERATORS Fild Feb. 27, 1951 WVEA/rw?PHIL/P T/V/c/rsm Patented Sept. 1953 CORRECTION DEVICE FoR FUNCTIONGENERATORS Philip T. Nickson, East Braintree, Mass., assignor toRaytheon Manufacturing Company, Newton, Masa, a corporation of DelawareApplication February 27, 1951, Serial No. 212,912

9 Claims.

Thisinvention relates to function generators and more particularly todevices for correcting certain errors in mechanical slide and linkagemultiplication and division function generators.

In mechanical slide and linkage multiplication and division functiongenerators of the type disclosed in the copending application, SerialNo. 190,456, filed October 17, 1950, by Sumner D. Lewis, one factor ofthe multiplication is entered either by an angular or by a lineardisplacement of the first input element which is communicated to asecond input member by a link. The angular displacement of the secondinput member represents the other factor of the multiplication. Thetotal resultant linear displacement of a slide member mounted in a sloton the second input member represents the product. This displacement istransmitted to a slide mounted in a slot on a fixed frame member by apivoted link connecting the slide members. Due to the geometry of themechanism, the. linkage joining the slide members on the rotatable inputand the fixed output members is positioned at different angles to theoutput slides path in its different positions. This output link rotatesabout its pivots on the slidable members. The vector distance betweenthe points of attachment of this link on the two slides remains constantbut because of the rotation the projection of this distance on thecenter line of the output slides slot varies as the cosine of the anglethe link makes with the center line of the fixed output slot. Thisprojection is not of a constant length and so a constant value is notadded to the displacement of the pivot point onthe slide member of therotating input member as the pivot point in the output slide isdisplaced. This deviation from a constant increment introduces an'errorinto the output. With small displacements of the inputs, this error isvery slight and may be ignored in many applications. However, withrelatively large displacements of the input, and in some applications,it becomes too great to be ignored.

This source of error is corrected in the present invention by adding anadditional link pivoted at the mid-point of the link joining the'slideson the rotatable input and the fixed output slide. This added link ismade one-half the length of the link to which it is joined. The lineardis placement of the slide joining the new link to the output slot isthe measure of the product of the multiplication. For geometric reasonsto be explained later, the'pivot point of the new slide lies at alltimeson a perpendicular line dropped from the pivot point of the slide on therotatable input member. As the input fixed slot is at right angles tothe output fixed slot, the displacement of the new slide is at all timesequal to the displacement of the slide on the rotatable input member.Thus this source of error is eliminated.

It is possible to further increase the accuracy of the multiplierby'pivotally attaching such a link to the mid-point of the link betweenthe input slide on the fixed input slot and the slide on the pivotedinput member. The other end of this added link is attached to a secondslide in the fixed input slot. This second input slide may be fittedinto a separate fixed slot collinear with the original input slot. Thisadded link is one-half the length of the link to which it is pivotallyattached. The displacement of the new slide measures the input. Asbefore, for geometric reasons, it is at all times on a perpendicularline dropped to the input slot center line from the slidable member ofthe pivoted input member. This removes the possibility of error due tothe varying angle of the link joining the input slide to the slidemember on the rotatable input member.

Thus by the addition of a link and slide member to either the input orthe output, or both,

of a mechanical slide and linkage multiplication and division functiongenerator, the accuracy of the device is considerably increased.

These, and other advantages, features and objects of the invention willbecome more apparent from the following description taken in connec tionwith the illustrative embodiments in the accompanying drawings, wherein:

Fig. 1 is an illustrative schematic diagram of one embodiment of theinvention;

Fig. 2 is a diagrammatic illustration of the principle of the invention;and

Fig. 3 is an illustrative schematic diagram of another embodiment of theinvention wherein a link and slide member have been added to the inputas well as to the output.

In referring to Fig. 1 for clarity of discussion, a particular set ofdimensions will be assigned to the various members. However, it shouldbe understood that such a linkage arrangement will act as an approximatemultiplier or divider for practically any linkage geometry that might beselected. Therefore, the dimensions used are intended to be illustrativeonly, and not restrictive. The illustrative embodiment in Fig. 1 whenused as a multiplier has first and second input memhers I!) and 12. Thefirst input member In is mounted to slide within a slot 13 in a framemember I4. The second input member I2 is pivoted to the frame Is at itand is formed with a slot I1 within which a slide [8 is mounted. A linkis pivotally fastened to slides Ill and H3 at points 2| and 22,respectively. The linear displacement of point 22 is communicated to aslide 23'fitted in a slot 24 in a frame member 25 by a link 26 pivotallyattached to the slide I8 at point 22 and to the slide 23 by pin 21.

At the center of link 26 a third link 28 is pivotally attached by pin30. This link 28 is attached at its other end to a slide 3| in the slot24 in frame member 25 by a pin 32.

The dimensions are selected for the various parts by the designprocedure described in the cited copending Lewis application. It is notthought necessary to repeat a description of this design procedure atthis point.

As more fully described in the copending Lewis application referred toabove, one factor of a multiplication is represented by the lineardisplacement of slide H) from the position represented by line 23 tothat represented by line 33, a distance represented by the dimension 34.The second factor is represented by the angular dislacement '6 of thepivoted input I2. The resuit is to displace the slide IB both angularlyand linearl along the slot IT. This displacement is communicated to theslide 23 by the link 26 and moves the pin 21 from the positionrepresented by the line 35 to that represented by the line 36, adistance represented by the dimension 31.

It Will be readily apparent from a consideration of the geometry of thearrangement that the displacement measured by the dimension 31 will notalways be equal to the displacement of the point of intersection 32 of aline dropped from point 22 perpendicular to the center line of the slot24. If this be true, the distance from point 32 to point 21 shouldalways be the same. This cannot be true because the distance from 32 to21 is a function of the angle, b, the center line of the link 26 makeswith the center line of the slot '24. More specifically, the distancefrom 32 ton equals the oils times the length of the link 26. Thus thedisplacement of the point 21 is not a true measure of the displacementof point22.

From the above it 'will be seen that, if a point on the center line cfthe slot 24 could be located that was always on the perpendicular linedropped to that line from the point 22, it would be an accurate indexOf'the linear displacement of the point 22 along a line parallel to thecenter line of the slot 24; The displacement of this point would beproportional atall times to the product of thei'nultiplication.

Such a point may be located by the linkage 28 of the present invention.This can best be seen by reference to Fig. 2wherein the output linkageis represented by a triangle in which point 22 is the center ofthe pin22, the point 21 is the centerof the pin 21, the point 32 is the centerof the pin 32, and point 30 is the center of the pin 30. The side of thetriangle joining points 22 and 21 is proportional to the length of thelink 26. The point 32 lies on the center line of the slot 24 and on theperpendicular line 40 dropped from the point 22 to the center line ofthe slide '24. The dimensions of the triangle in Fig. 2 are proportionalto the corresponding dimensions of the linkages in Fig 1, and thecorresponding angles of the two figures ar equal. If the length of thelink 261s taken to be '2: and the distance from point 32 to point 21 istaken to 4 be a, and the angle between the link 26 and the center lineof the slot 24 as A, then a=cos Am. As explained before, a: is aconstant and A is a variable depending upon the settings of the inputslide Ill and the input member [2. Thus a is a variable.

If the point .30 is located at the midpoint of the link 26 and the line.28 drawn between it and the center line of the slot 24 and has a lengthequal to one-half the length of link 26, two isosceles triangles areformed, one joining the points 22, 30 and 32 and the other the points21, 30 and 32. Of the first-mentioned triangle, the sides joining thepoints 22 and 30, and 30 and 32 are equal to each other, each beingequal to one-half the length of link 26. Thus the angles D and Eopposite these sides are equal. Of the secondmenticned triangle, thesides joining the points 21 and 3D, and points 30 and 32 are equal, aseach is one-half the length of "the link 26 by construction. As before,the angles A and B opposite each of these sides will be equal also. Byconstruction,

F+ c=l as the link 26 is a straight line. Also A+ B+ C=' "(1) and D+ E+F=180 (2 substituting equals for equals:

2B+C==180 43 2D+F 180 (4) Adding (3) and 4), 2B+C+F+2D=360 substituting,2B+2D+180=360 simplifying, 2B+2D=180 dividing throughby 2, B+D=9U Thusthe line joining point 22 and point 32 is perpendicular to the'centerline of the slot 24 at all times. Thus it hasrbeen seen that theaddition of the link 26 locates a point '32 on the center line of theslot 24 having the same perpendicular distance from theslide I 3 as thepoint is at various angles ,4)" tocthe center line of slot [3, theparticular angle-depending upon the relative positions-of the slidesHlwand 1'8. Again this can be corrected byprovidin a means by which theslide input is always maintained-on a perpendicular line dropped from: apoint 22 to the center line of the slot [3. As shown in Big. 3, this isprovided by the-link, pi-votally attached at one end to the center pointof the link 28 :by a pin 42 and at the other end to aslide 43 intho slotI 3 by the pin 44. The link 4|, as beforeris made one-half thelength ofthe link 20 to which it is attached: The slot-inwhich the slide '43: itis travels need not be thesame as slot 13. sufficient if it is collinearwith it. A proofsimilar to that used for the link 28 will show that thecenter point of the pin 44 will'always lie at the intersection of.asline 4.5 dropped from the point '22 perpendicular to the center lineof theslot I3.

For simplicity of explanation, the center'lines of the slots 13 andit;have been 's'hownas er,

accents pendicular to each other pivot point I8 of the input element l2."This condition is not necessary to the operation of the multiplier.However, any other configuration introduces other possibilities oferrors that must be accounted for in the design of the equipment bymethods that are no part of the presentinven Lewis application, thebasic structure described as a multiplier may be used as a divider byinserting a dividend in the form of displacement 31 of the slide 23 andinserting the divisor by displacing either slide or rotating inputmember [2 with the resulting displacement of the unused element In or l2as the output. The added link 28 or 4| and slide 3! or 43 serve the samepurpose of increasing the accuracy in the mechanism when used fordivision as when used for multiplication.

It is readily apparent that the correction device of the invention canbe used wherever linear displacement must be transmitted accuratelybetween a slide in a fixed slot and a slide in a rotating element. Itsuse in a multiplication and division device of the type disclosed in theLewis application is one of several possible applications.

This invention is not limited to the particular details of construction,materials and processes described, as many equivalents will suggestthemselves to those skilled in the art. It is accordingly desired thatthe appended claims be given a broad interpretation commensurate withthe scope of the invention within the art.

What is claimed is:

1. A correction device for a function generator of the type having twomechanical displacement inputs, one of which comprises a rotary elementcarrying a slide in a slot, the center line of which passes through thepivot of the rotary element, and an output element comprising a fixedelement formed with a slot carrying a slide and a linkage member joiningthe slides, said correction device comprising a third slide adapted totravel in a slot collinear with the slot in the fixed element and a,second linkage member half the length of the first-mentioned linkagemember and engaging the mid-point of said linkage member and thethird-mentioned slide.

2. A correction device for a two variable multiplier and divider systemof the type having mechanical displacement input members, one of whichinserts the valve of one of said variables as an angular displacementquantity, said input member having a pivot point and carrying a slide ina slot, the center line of the slide passing through the pivot point, amechanical output member for indicating the answer as a lineardisplacement quantity, slide means coupled to said angular displacementinput member, and a linkage member engaging said slide means and outputmember, thereby causing mechanical cooperation between said input andoutput members for producing said answer, comprising a second slidemeans adapted to move collinearly with the linear displacement of thesaid output member and a linkage member half the length of the linkagemember engaging said slide'means and output member joining the mid-pointof said linkage to the second slide means to accurately represent thelinear displacement of the first-mentioned slide means and thus theanswer.

3. A correction device for a function generator having a first slidablymounted input member, a .second pivotally mounted rotative input member,

and intersecting at the output means, and a connecting link engagingsaid slide means and output means, comprising a third slide meansadapted to move collinearly with the linear displacement of the saidslidably mounted input member and a third connecting link half thelength of the first-mentioned connecting link'connected between themid-point of said first-mentioned connecting link and the third slidemeans to accurately communicate its linear displacement to the slidemeans on the second input member.

4. A correction device for a function generator having a first slidablymounted input member, a second pivotally mounted rotative input member,slide means on said second member, the center line of which passesthrough the pivot of the rotative member a connecting link engaging saidfirst member and slide means, slidably mounted output means and aconnecting link engaging said slide means and output means, comprising,a third slide means adapted to move collinearly with the lineardisplacement of the said slidably mounted input member and a thirdconnecting link half the length of the first-mentioned connecting linkconnected between the mid-point of said first-mentioned connecting linkand the third slide means to accurately communicate its lineardisplacement to the slide means on the second input member, and a fourthslide means adapted to move collinearly with the displacement of thesaid slidably mounted output member and a fourth connecting link halfthe length of the second-mentioned connecting link connected between themid-point of said second-mentioned connecting link and the fourth slidemeans to accurately represent the linear displacement of the slide meanson said second input member and thus the function. I

5. A correction device for a two variable multiplication and divisionfunction generator of the type having a first slidably mounted inputmember, a second pivotally mounted rotative input member, slide means onsaid second member causing movement along a center line through saidpivotal mounting, a connecting link engaging said first member and slidemeans, slidably mounted output means, and a connecting link engagingsaid slide means and output means, said correction device comprising vasecond slidably mounted output means adapted to move collinearly withthe first said means and a third connecting link half the length ofsecond said connecting link engaging the mid-point of said secondconnecting link and said second slidably mounted output means toaccurately transmit the linear displacement of said slide means toindicate the value of the function.

6. A correction device for a two variable multiplication and divisionfunction generator of the type having a first slidably mounted inputmember, a second pivotally mounted rotative, input member, slide meanson said second member causing movement along a center line through saidpivotal mounting, a connecting link engaging said first member and slidemeans, slidably mounted output means, and a connecting link engagingsaid slide means and output means, said correction device comprising asecond slidably mounted input member adapted to move collinearly withthe first, a third connecting link half the length of thefirst-mentioned connecting link and engaging: the. midrpoi-nt ofi thefiISt -QIIEIIe tionedconnecting link. and the. seeondslidably mountedinput member to, accurately transmit, the. linear displacement of. the.slidable input. member tothe second pivotally mounted. rotati-ve inputmember, and a second.. slidably mounted. output member adapted. to; movecol-linearly with. the first, a fourth connecting link. halt the length.of, the seeondi-mentionedl connecting link and engaging; the.- mid-pointof the secondementioned; connecting? link and. the second slidablymounted. output member to acct-trateh; transmit, the linear displacementof. the; said slide means to indicate: the; value of the function.

'7. A correction device for a two variable multiplica-tion and diuisioniiunction generator of the typehaving a first slidably mounted inputmenu-- her asecond. pivotally mounted. rotative input member, slidemeanson. saidsecond member causing movement along. a center line throughsazidpivotat mounting, a connecting, link. engaging said first member.and slide means;v slidably mountedoutput-means disposed to move in a.di- P80131011. perpendicular to said slidably mountedv input member, anda. commecting link engaging. said: slide means and output means,comprising. a second slidabiy'mounted output means disposed tomove.coll-measly with. the first-mentlonedslid-- ably mounted output. meansand, athird connecting: link halfthe. length. of the. secondsmentioned.connecting: linker-leasing, the. mid-point of said second connecting.link. and the. second-mentinned. slidazbly' mounted output. means, toaccurately transmit the linear displacement of the. said slide-means toindicate the value of the function..

8:. A. correction device for a. two variable. multiplicationand-division function.- generator of. the typehavingafirstslidablymounted. input member, a secondpivotally mountedrotatiye input member, slide means on said secondv member causingmovement along a center line. through said pivotal mounting, a.connecting; link engaging said first member and slide. means, slidablymounted output means. disposedto. move inav direction perpendicular tosaid slidably mounted. input member, and. a connecting link engagingsaid slide. means and. output. means, comprising, a. second. slidablymounted input means. disposed to move collinearly withthefirst-mentioned slidably mountedinput means anda third connecting.link. halt the lengthoi the first-mentioned. con- Maine l en a in the.mid-point of said firstmentioned connecting link. and. the second slidably mounted input means to accurately transmit the; linear displacementof said slid'abl'y mounted input means to the slide. means on the secondrotatively mountedinput means 9-; Accrrection devicefor a. two variablemultiplication and division function generator of the tame. havinga-fi-rst'slidably mounted input, member, a second pivotally mountedrotative input,

member, slide means onsaid second member cansinemoumnent. along a centerline through said pivotal mounting, aconneeting, link en a in said firstmember and slide means, slidably mounted. output means disposed. to.move. in. a diperpendicular to said" slidably mounted inputmember,. anda connecting link engaging saidslidemeans and output means, comprising asecond slidabliy vmountedinput. means disposed to move collinearly withthe first-mentionedslidably mounted input means, a third. connectinglink hall? the. length oi the first-mentioned. connecting,linktengaging, the mid-point of said firstmentioned connecting link andthe second slidably mountedinput means to accurately transmit the lineardisplacement of said slidably mounted input, meansto the slide means onthe second rotatiuel-y mounted input. means, a second slid'ably mounted.input member adapted. to mov collinearly with thefirsttanda secondsliclably mounted output member adapted to move collinearly with thefirst, a iburthconnectihg. link half the length of the secondrmentioned'connecting link and engaging the. midpoint. of the second-mentionedconnecting link and. the second slidably mounted. output member toaccurately transmit the linear. displacement of the. said. slide meansto. indicate the value of the function.

'I'. NICKSONL References Cited" in the file of this patent UNITED.STATES PATENTS

